# Reversing Plot Axis with scientific Notation

I'm dealing now with a problem of three steps which already has solutions in each of them. Basically, I want to write numbers on x-axis with scientific notation, but before that, I reverse the axis following this reversing plot axis for Plot, LogPlot, LogLogPlot, afterwards I add a new scale with a function relating two time scales (the x axis) following How to make plot with frame and two different scales on the x-axis (CMB power spectrum example)

1. So first of all I defined two functions, the first one to properly reverse the plot, and the second one which give the rescaling in the axis

 ze[t_] = 10^(9)*Exp[0.68 - t] - 1;
zp[t_] = -t + 25;


lets plot an arbitrary function (in my case is the solution of a system of 5 coupled ODE's)

    Needs["MaTeX"]

fx[t_] = 3 t - Exp[t + 2];

Plot1 = Plot[fx[zp[t]], {t, 0, 25},
PlotStyle -> {Directive[Thick, Red, DotDashed]}, Frame -> True,
Axes -> False,
FrameLabel -> {(MaTeX[#, Magnification -> 2.6] &) /@
Style["\\mathcal{T}"]}, RotateLabel -> False,
FrameStyle -> BlackFrame,
BaseStyle -> {FontFamily -> "Times New Roman", FontSize -> 15
},
PlotLegends -> Placed[LineLegend[{
Directive[Thick, Red, DotDashed]}, {
(MaTeX[#, Magnification -> 1.6] &) /@ Style["f_x"]},
LegendLayout -> {"Row", 1}, LabelStyle -> {Black, Bold, 15},
LegendFunction -> Frame],
{0.46, 0.28}], ImageSize -> 400, AspectRatio -> 1,
FrameTicks -> {{Automatic,
None}, {Transpose[{Range[0, 25, 5],
N@ze[#] & /@ Range[0, 25, 5]}], Range[0, 25, 5]}}] (the gray comes from the style I'm using on the notebook). This plot then is inverted in the axis (by function zp[t]) and with and additional scale. So my problem is to put that ugly horizontal scale (reescaled by the function ze[t]) in scientific notation. I tried to used CustomTicks, but perhaps I'm missing something. Appreciate any help

• does FrameTicks -> {{Automatic, None}, {Transpose[{Range[0, 25, 5], ScientificForm[ze[#], 2] & /@ Range[0, 25, 5]}], Range[0, 25, 5]}} give what you need? – kglr Jan 29 at 5:57
• Dear @kglr, thanks a lot... this is almost what I want (maybe I should clarify that) Or maybe I'm adding an innecesary step. Can I just represent that scale in sort of Logaritmic one? Actualy the plot I need (with my calculations) should be LogLinearPlot. – Alejandro Guarnizo Jan 29 at 6:06
• you mean something like this: LogLinearPlot[fx[zp@Exp[t]], {t, 1, Log@25}, PlotStyle -> {Directive[Thick, Red, DotDashed]}, Frame -> True, Axes -> False, AspectRatio -> 1]? – kglr Jan 29 at 6:13
• or Plot[fx[t], {t, 0, 25}, PlotStyle -> {Directive[Thick, Red, DotDashed]}, Frame -> True, Axes -> False, AspectRatio -> 1, ScalingFunctions -> {"Reverse", None}]`? – kglr Jan 29 at 6:34